Brakke inequality and the existence of Brakke-flow for volume preserving mean curvature flow
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arXiv
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| Format: | Preprint |
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2025
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| _version_ | 1866908384211501056 |
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| author | Chiesa, Andrea Takasao, Keisuke |
| author_facet | Chiesa, Andrea Takasao, Keisuke |
| contents | In this paper, we propose a new notion of Brakke inequality for volume preserving mean curvature flow. We show the existence of integral varifolds solving the flow globally-in-time in the corresponding Brakke sense using the phase field method. Morever, such varifolds are solutions to volume preserving mean curvature flow in the $L^2$-flow sense as well. We thus extend a previous result by one of the authors [25]. |
| format | Preprint |
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arxiv_https___arxiv_org_abs_2505_23222 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Brakke inequality and the existence of Brakke-flow for volume preserving mean curvature flow Chiesa, Andrea Takasao, Keisuke Analysis of PDEs 35K93, 53E10 In this paper, we propose a new notion of Brakke inequality for volume preserving mean curvature flow. We show the existence of integral varifolds solving the flow globally-in-time in the corresponding Brakke sense using the phase field method. Morever, such varifolds are solutions to volume preserving mean curvature flow in the $L^2$-flow sense as well. We thus extend a previous result by one of the authors [25]. |
| title | Brakke inequality and the existence of Brakke-flow for volume preserving mean curvature flow |
| topic | Analysis of PDEs 35K93, 53E10 |
| url | https://arxiv.org/abs/2505.23222 |